where \(\Theta _l\)  is the dihedral angle around the edge \(e\)  (dual to link \(l\) ) and \(V\)  is the volume of the tetrahedron with edge length \(\ell _l=\lambda j_l+2\,,l=1,\cdots , 6\)  (see also Section REF  for a more detailed analysis).
This asymptotic was postulated by Ponzano and Regge [1]} and proven in different methods [2]}, [3]}, [4]}, [5]}. The Hartle-Sorkin action (REF ) is the discrete version the GHY boundary term [6]}:
\(\int _{\partial {\mathcal {M}}} \mathrm {d}^2 \sqrt{h}K\xrightarrow{} \sum _{l\in (\partial \triangle )^*_1} \ell _l\Theta _l\,.\) 
